Related Rates: Calculating Height and Radius of a Conical Pile

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Homework Statement


Sand falls from a conveyor belt at the rate of 10 m^3/min onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the a) height and b) radius changing when the pile is 4m high?


Homework Equations


h = 3/8 * 2r


The Attempt at a Solution


I'm not sure where to start. I just need a small hint.
 
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The question is giving you dV/dt. What's the equation for the volume of a cone in terms of r and h? That's a small hint.
 
More than enough. Thanks
 
The rate of change of the volume of the cone is 10 m3 per minute. What is the expression for the volume of a cone in terms of its height and base radius? This will allow you determine dr/t or dh/t in terms of dV/dt.

EDIT: two minutes too late...
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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